Barkley struck in the 2-2 draw at Norwich City yesterday.
"He's been at Everton for a long time and he's had his problems with injuries," Martinez said.
"I can only speak about his attitude and the way he looks after himself and the way he works in pre-season. I'm pleased he's been able to show everyone he's ready.
"That's what important about his play. He can understand what he needs to do to be effective off the ball. He wants to take information in and wants to understand. I thought he was perfect at it today."
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